You could estimate the initial pressure of an inactive element (i.e., the constant pressure specified as a Dirichlet b.c.); use command >> INITIAL PRESSURE.
Estimating the generation rate of an element with a large volume only makes sense if you employ Karsten's approach for specifying time-dependent Dirichlet b.c.s, which requires that you use very large generation rates. You can certainly estimate these rates as well; use command >> RATE.
You cannot estimate generation rates of an inactive element (i.e., an element following one with a zero volume), as (by definition!) it won't affect the output.
If you are asking about the flow rates from a boundary element, these would be observations (i.e., not estimatable parameters).
Thanks Stefan! Ideally what I'm trying to set up is a constant pressure held in a reservoir (call it A) that is emptying through a porous, permeable barrier into another confined porous space (call it B). I'll be able to monitor both the pressure in A (i.e., how close I'm holding it to constant, possibly requiring time-dependent BC's) and the flow rate into A necessary to maintain this "constant" pressure setting. I should also be able to calculate (through TOUGH) what the flow rate going into B is based on its pressure response, so the difference between the observed outflow rate from A and the calculated flow rate into B should give an indication of how much is leaking out (or produced). I was just wondering if iTOUGH would have a way to resolve all of this for me, so I could more effectively use the monitored flow rates as additional observation data to acquire estimates of the parameters I'm really interested in.Reply
The somewhat confusing part is whether you want the pressure A (a) to be prescribed (either constant or time dependent) or (b) let it vary and observe it. I understand that you do both in the lab, but you need to decide whether it is (a) or (b) if it comes to modeling and inversion. If it is (a), we are talking about an input PARAMETER; if it is (b), it is output an OBSERVATION. Of course, you can also specify the pressure in A as an input and at the same time extract the pressure in A as an observation - even though you already know the outcome of that!
Here is what I think you want to do:
(1) As your reservoir A is not really “inactive” or infinitely large, give it its actual volume.
(2) Specify a flow rate into A (this is your way of “maintaining” the pressure in A, right?); let’s call it Q_A.
(3) Make Q_A an adjustable parameter in iTOUGH2 using command > PARAMETER, >> RATE.
(4) Add the pressure in A as an observable variable, > OBSERVATION, >> PRESSURE; let’s call it P_A.
(5) Add the actually measured pressures in A as a function of time in block >>>> DATA.
(6) Specify a sufficiently small standard >>>> DEVIATION to these pressure data.
With this setup, the model will adjust Q_A such that it closely tracks P_A.
You can also revert the whole thing, i.e., make P_A an adjustable input parameter and Q_A the observations to be matched, but (1)-(6) above seems more natural and easier to implement.
In general, it is always important to decide what is an input parameter and what is an output observation. Finally, keep in mind that input parameters can also be treated as observations through the concept of >>>> PRIOR information (i.e., by using command >>>> DEVIATION instead of >>>> VARIATION in the > PARAMETER block).
Hope this make sense…
What you say makes sense. The only issue I'll have is that, by following your procedure (1-6) in the lab, the observed Q_A will be characteristically different than the modeled Q_A required to maintain the prescribed P_A due to system leaks. In other words, the flow that gets provided by the pump into A offsets both the ingress into the permeable barrier separating it from B (the modeled Q_A) and the leaks from the system into the ambient surroundings.
I should also note that I'll be observing the pressure in B.
It's entirely possible (and perhaps likely) that I can maintain good pressure control, prescribe Dirichlet conditions in my model and infer the properties I'm interested from P_B data only. However, I wanted to know the best way to make use of the observable Q_A data while still accounting any leaks that may take place.Reply
I do not quite see how the leakage issue is specific to approach (a).
As you know, I consider it an essential part of inverse modeling to make sure that modeled and measured quantities are conceptually consistent. That means that you either have to fix the leak in your apparatus, or represent the leak in your model (and potentially include the unknown leakage rate in your estimation process). Specifically since you have pressures (and outflow rates?) in B, this should be possible.